Critical behavior of (1+1)-dimensional transverse Ising models for spinS≥12

Abstract

The phase transitions in the ground state of (1+1)-dimensional Ising models in a transverse field are investigated for spin $S=\frac{1}{2}, 1, \frac{3}{2}, \mathrm{and} 2$. The critical fields and "thermal" and correlation exponents are calculated as a function of $S$ by the finite-size scaling method. The universality of the transition with respect to $S$ is fully confirmed. Furthermore, we elaborate on a recent conjecture by Luck and others relating the correlation exponent $\ensuremath{\eta}$ to the amplitude of a correlation length for a two-dimensional (2D) classical isotropic system. The extension of this relation to quantum chains as extremely anisotropic 2D systems has been considered. We find that while no simple prescription can be given to calculate various correlation exponents from the amplitudes, the ratios of the amplitudes of different quantities still have universal character.